Question
A ball has a 75% rebound ratio. When you drop it from a height of 16 ft, it bounces and bounces...
When it strikes the ground for the second time, the ball has traveled a total of 28 ft in a downward direction. How far downward has the ball traveled when it strikes the ground for the 17th time?
When it strikes the ground for the second time, the ball has traveled a total of 28 ft in a downward direction. How far downward has the ball traveled when it strikes the ground for the 17th time?
Answers
MathMate
T(1)=16
T(2)=12
T(3)=9
...
T(n)=16(3/4)^(n-1)
It is a geometric progression (GP) with a ratio of 3/4.
The sum to n terms of a GP is:
S(n)=16(1-(3/4)^n)/(1-(3/4))
Substitute n=17 in the above formula to get S(17), the <i>total</i> downward distance.
T(2)=12
T(3)=9
...
T(n)=16(3/4)^(n-1)
It is a geometric progression (GP) with a ratio of 3/4.
The sum to n terms of a GP is:
S(n)=16(1-(3/4)^n)/(1-(3/4))
Substitute n=17 in the above formula to get S(17), the <i>total</i> downward distance.